ACM Transactions on

Computational Logic (TOCL)

is devoted to research concerned with all uses of logic in computer science. Logic continues to play an important role in computer science and permeates many of its areas including: artificial intelligence, computational complexity, database systems and programming languages

This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features of hybrid systems and discrete games, but only deterministic differential equations. Differential games,... (more)

Continuous Petri nets are a relaxation of classical discrete Petri nets in which transitions can be fired a fractional number of times, and consequently places may contain a fractional number of tokens. Such continuous Petri nets are an appealing object to study, since they over-approximate the set of reachable configurations of their discrete... (more)

We consider recursion schemes (not assumed to be homogeneously typed, and hence not necessarily safe) and use them as generators of (possibly... (more)

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About
TOCL welcomes submissions related to all aspects of logic as it pertains to topics in computer science. The journal is published quarterly. The first issue appeared in July 2000, and the journal is indexed by ISI beginning with the 2006 volume. About

We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of structures such that the first structure is an element of A. We present a comprehensive complexity classification of these problems, which strongly links graph-theoretic properties of A to the complexity of the corresponding homomorphism problem. In particular, we define a binary relation on graph classes, which is a preorder, and completely describe the resulting hierarchy given by this relation. This relation is defined in terms of a notion which we call graph deconstruction and which is a variant of the well-known notion of tree decomposition. We then use this hierarchy of graph classes to infer a complexity hierarchy of homomorphism problems which is comprehensive up to a computationally very weak notion of reduction, namely, a parameterized version of quantifier-free first-order reduction. In doing so, we obtain a significantly refined complexity classification of homomorphism problems, as well as a unifying, modular, and conceptually clean treatment of existing complexity classifications. We then present and develop the theory of Ehrenfeucht-Fraisse-style pebble games which solve the homomorphism problems where the cores of the structures in A have bounded tree depth. Finally, we use our framework to classify the complexity of model checking existential sentences having bounded quantifier rank.

In this paper we propose a new technique for checking whether the bottom-up evaluation of logic programs
with function symbols terminates. The technique is based on the definition of mappings from arguments to strings of function symbols,
representing possible values which could be taken by arguments during the bottom-up evaluation.
Starting from mappings, we identify mapping-restricted arguments, a subset of limited arguments, namely arguments which
take values from finite domains. The class of mapping-restricted programs, consisting of programs whose arguments are all mapping-restricted, is terminating under the bottom-up computation as all its arguments take values from finite domains.
We show that mappings can be computed by transforming the original program into a unary logic program: this allows us to establish decidability of checking if a program is mapping-restricted. We study the complexity of the presented approach and compare it with other techniques known in the literature. Furthermore, we introduce an extension of the proposed approach which is able to recognize a wider class of logic programs as terminating. The presented technique is relevant as it individuates as terminating programs not detected by other criteria proposed so far and can be combined with other techniques to further enlarge the class of programs recognized as terminating under the bottom-up evaluation.

In this paper, we consider the setting of graph-structured data (GSD) that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from deciding whether a given sequence of actions preserves the satisfaction of a given set of integrity constraints, for every possible initial data instance, to deciding the (non-)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. For describing states of the data instances and expressing integrity constraints on them, we use Description Logics (DLs) closely related to the two-variable fragment of first-order logic with counting quantifiers. The updates are defined as \emph{actions} in a simple yet flexible language, as finite sequences of conditional insertions and deletions, which allow one to use complex DL formulas to select the (pairs of) nodes for which (node or arc) labels are added or deleted. We formalize the above data management problems as a static verification problem and several planning problems and show that, due to the adequate choice of formalisms for describing actions and states of the data, most of these data management problems can be effectively reduced to the (un)satisfiability of suitable formulas in decidable logical formalisms. Leveraging this, we provide algorithms and tight complexity bounds for the formalized problems, both for expressive DLs and for a variant of the popular DL-Lite, advocated for data management in recent years.